Ittol Foudto Y (IFY) IFYFM00 Futh Mths Appd C Fomul Booklt Rltd Documts: IFY Futh Mthmtcs Syllbus 07/8
Cotts Mthmtcs Fomul L Equtos d Mtcs... Qudtc Equtos d Rmd Thom... Boml Epsos, Squcs d Ss... Idcs, Epotl d Logthmc Fuctos... Tgoomtc Fuctos d Idtts... Dtto...4 Itgto...5 Vctos...6 Numcl mthods...6 Itoducto to Sttstcs...7 Futh Mthmtcs Fomul Pls ot tht th ltts gv th hdg o ch scto to th topc o th syllbus to whch th omul lt. A & L - Compl Numbs...8 B - Mtcs...8 D & J - Ss...9 G - Hypbolc Fuctos... 0 I - Coc Sctos... 0 M - Futh Dtto d Itgto... N - Vctos... Sttstcl Tbls Noml Dstbuto Tbl... Tl Pobblty P... 4
IFYFM00 Futh Mthmtcs Appd C Fomul Booklt Mthmtcs Fomul L Equtos d Mtcs Stght L y m c, wh m s th slop o gdt, d c s th y -tcpt L though pots 0, y 0, y d y y 0 0 y y 0 0 Ivs o mt I b d b A, th A c d d bc c d bc Qudtc Equtos d Rmd Thom Qudtc Fomul I b c 0, th b b 4c 0 07 Noth Cosotum UK Ltd. Pg o 4
IFYFM00 Futh Mthmtcs Appd C Fomul Booklt Boml Epsos, Squcs d Ss Boml Ss Wh s postv tg, ( b) b b... b b ( b) 0 b C!!( )! Wh s ot postv tg ( ) ( )( ) ( )...,!! Athmtc Ss (AP) s th st tm, d s th commo dc th tm: u ( ) d, Sum to tms: S ( ( ) d) Gomtc Ss (GP) povdd, R. s th st tm, s th commo to th tm: u Sum to tms: S ( ) Sum to ty: S, povdd 07 Noth Cosotum UK Ltd. Pg o 4
IFYFM00 Futh Mthmtcs Appd C Fomul Booklt Idcs, Epotl d Logthmc Fuctos log log log b b l Tgoomtc Fuctos d Idtts s cos b c bc cos A s A s B b s C c Doubl gl: s s cos cos cos s s cos Sums d dcs: s( A B) s Acos B cos As B cos( A B) cos Acos B s As B t A t B t( A B) t At B 07 Noth Cosotum UK Ltd. Pg o 4
IFYFM00 Futh Mthmtcs Appd C Fomul Booklt Dtto () k l s cos t d ( ) d ( ) ( ) () ( ) d d sc sc t k k csc csc cot cot csc cos s s cos sc t Ch Rul: I y s ucto o u d u s ucto o, th dy d dy du. du d Poduct Rul: I y uv, wh u d v uctos o, th dy d du dv v u d d Quott Rul: I u y v wh u d v uctos o, th du dv v u dy d d d v 07 Noth Cosotum UK Ltd. Pg 4 o 4
IFYFM00 Futh Mthmtcs Appd C Fomul Booklt Itgto (), l l b s cos cos t ( ) d () b sc csc cot s l cos ( ) d l sc t l csc cot l s s, t Itgto by pts dv u d uv d Applctos o tgto du v d d A ud cuv: Volum o voluto: A b y d b V y d 07 Noth Cosotum UK Ltd. Pg 5 o 4
IFYFM00 Futh Mthmtcs Appd C Fomul Booklt Vctos Ut vcto â th dcto o ˆ, wh s th modulus (mgtud) o. Scl Poduct. b b cos wh s th gl btw d b.. b b. I j k d b b b j b k, wh, j d k ut vctos th, y d z dctos, th. j.j k.k,. j jk. k. 0,.b, b b b.. I both d b o-zo vctos th s ppdcul to b.b 0. Numcl mthods Soluto o ( ) 0 gv 0, Nwto-Rphso: ( ) ( ) 0,,, 07 Noth Cosotum UK Ltd. Pg 6 o 4
IFYFM00 Futh Mthmtcs Appd C Fomul Booklt 07 Noth Cosotum UK Ltd. Pg 7 o 4 Itoducto to Sttstcs Msus o vg d spd Ugoupd Dt Goupd Dt M Vc Stdd Dvto Chg o og/scl : I ) ( k X, th ) ( k X X k.
IFYFM00 Futh Mthmtcs Appd C Fomul Booklt Futh Mthmtcs Fomul A & L - Compl Numbs z y cos s cos s wh cos s Th oots o z gv by k z o k 0,,,,. Th symbol j s lso usd to dot B - Mtcs L tsomtos Rlcto bout th - s: 0 0 Rlcto bout th y- s: 0 0 Rlcto bout th l y = : 0 0 Atclockws otto though gl bout th og: cos s s cos Ivs o mt d g b h c A D G B E H C F I T, wh d g b h c 07 Noth Cosotum UK Ltd. Pg 8 o 4
IFYFM00 Futh Mthmtcs Appd C Fomul Booklt D & J - Ss Mclu Ss 6 4 ( ) Gl ss: ( ) (0) (0) (0)... (0)...!!!...!..., o ll l( )... ( ), s! 5 5!... ( )..., ( )! o ll 4 cos... ( )! 4!..., ()! o ll ct 5 5, Tylo ss 5 sh......,! 5! ( )! 4 cosh......,! 4! ()! o ll o ll!! o!! 07 Noth Cosotum UK Ltd. Pg 9 o 4
IFYFM00 Futh Mthmtcs Appd C Fomul Booklt G - Hypbolc Fuctos cosh sh cosh sh sh sh cosh, cosh cosh sh sh l( ) cosh l( ), th l, I - Coc Sctos Cts Fom Pmtc Fom Ecctcty Foc,0 Pbol Ellps Rctgul Hypbol y 4 y y c b ( t,) t ( cos, bs) c ct, t (,0 ) ( c, c ) Dct Dctcs Asymptots 0, y 0 07 Noth Cosotum UK Ltd. Pg 0 o 4
IFYFM00 Futh Mthmtcs Appd C Fomul Booklt M - Futh Dtto d Itgto Dtto () d ( ) ( ) d sh cosh cosh sh th sch sh cosh th Itgto () sh cosh th ( ) d cosh sh l cosh sh cosh, th Ac lgth: L Suc o voluto wh th c th -s: dy d d d dt dy dt dt y s ottd though ds bout S y ds y dy d y d d dt dy dt dt 07 Noth Cosotum UK Ltd. Pg o 4
IFYFM00 Futh Mthmtcs Appd C Fomul Booklt N - Vctos Vcto Poduct b b s, wh s th gl btw d b, ppdcul to both d b. d s ut vcto b b I j k d b b b j b k, wh, j d k ut vctos th, y d z dctos, th j j k k 0, j k, jk, k j, b b b ) ( b b ) j ( b ) k. ( b I both d b o-zo vctos th s plll to b b 0. 07 Noth Cosotum UK Ltd. Pg o 4
IFYFM00 Futh Mthmtcs Appd C Fomul Booklt Noml Dstbuto Tbl I Z hs oml dstbuto wth m = 0 d vc =, th tbl gvs th pobblty, p tht Z s lss th o qul to z. z 0 0.0 0.0 0.0 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 0.5080 0.50 0.560 0.599 0.59 0.579 0.59 0.559 0. 0.598 0.548 0.5478 0.557 0.5557 0.5596 0.566 0.5675 0.574 0.575 0. 0.579 0.58 0.587 0.590 0.5948 0.5987 0.606 0.6064 0.60 0.64 0. 0.679 0.67 0.655 0.69 0.6 0.668 0.6406 0.644 0.6480 0.657 0.4 0.6554 0.659 0.668 0.6664 0.6700 0.676 0.677 0.6808 0.6844 0.6879 0.5 0.695 0.6950 0.6985 0.709 0.7054 0.7088 0.7 0.757 0.790 0.74 0.6 0.757 0.79 0.74 0.757 0.789 0.74 0.7454 0.7486 0.757 0.7549 0.7 0.7580 0.76 0.764 0.767 0.7704 0.774 0.7764 0.7794 0.78 0.785 0.8 0.788 0.790 0.799 0.7967 0.7995 0.80 0.805 0.8078 0.806 0.8 0.9 0.859 0.886 0.8 0.88 0.864 0.889 0.85 0.840 0.865 0.889.0 0.84 0.848 0.846 0.8485 0.8508 0.85 0.8554 0.8577 0.8599 0.86. 0.864 0.8665 0.8686 0.8708 0.879 0.8749 0.8770 0.8790 0.880 0.880. 0.8849 0.8869 0.8888 0.8907 0.895 0.8944 0.896 0.8980 0.8997 0.905. 0.90 0.9049 0.9066 0.908 0.9099 0.95 0.9 0.947 0.96 0.977.4 0.99 0.907 0.9 0.96 0.95 0.965 0.979 0.99 0.906 0.99.5 0.9 0.945 0.957 0.970 0.98 0.994 0.9406 0.948 0.949 0.944.6 0.945 0.946 0.9474 0.9484 0.9495 0.9505 0.955 0.955 0.955 0.9545.7 0.9554 0.9564 0.957 0.958 0.959 0.9599 0.9608 0.966 0.965 0.96.8 0.964 0.9649 0.9656 0.9664 0.967 0.9678 0.9686 0.969 0.9699 0.9706.9 0.97 0.979 0.976 0.97 0.978 0.9744 0.9750 0.9756 0.976 0.9767.0 0.977 0.9778 0.978 0.9788 0.979 0.9798 0.980 0.9808 0.98 0.987. 0.98 0.986 0.980 0.984 0.988 0.984 0.9846 0.9850 0.9854 0.9857. 0.986 0.9864 0.9868 0.987 0.9875 0.9878 0.988 0.9884 0.9887 0.9890. 0.989 0.9896 0.9898 0.990 0.9904 0.9906 0.9909 0.99 0.99 0.996.4 0.998 0.990 0.99 0.995 0.997 0.999 0.99 0.99 0.994 0.996.5 0.998 0.9940 0.994 0.994 0.9945 0.9946 0.9948 0.9949 0.995 0.995.6 0.995 0.9955 0.9956 0.9957 0.9959 0.9960 0.996 0.996 0.996 0.9964.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.997 0.997 0.997 0.9974.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.998.9 0.998 0.998 0.998 0.998 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990. 0.9990 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.999. 0.999 0.999 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995. 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998.5 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998 0.9998.6 0.9998 0.9998 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999.7 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999.8 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999 0.9999.9.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000 07 Noth Cosotum UK Ltd. Pg o 4
IFYFM00 Futh Mthmtcs Appd C Fomul Booklt Tl Pobblty P Dg o Fdom 0.40 0.0 0.0 0.5 0.0 0.05 0.05 0.0 0.05 0.0 0.0075 0.005 0.005 0.0005 0.5 0.77.76.96.078 6.4.706 5.895.05.8 4.4 6.657 7. 66.69 0.89 0.67.06.86.886.90 4.0 4.849 5.64 6.965 8.07 9.95 4.089.599 0.77 0.584 0.978.50.68.5.8.48.896 4.54 5.047 5.84 7.45.94 4 0.7 0.569 0.94.90.5..776.999.98.747 4.088 4.604 5.598 8.60 5 0.67 0.559 0.90.56.476.05.57.757.00.65.64 4.0 4.77 6.869 6 0.65 0.55 0.906.4.440.94.447.6.89.4.7.707 4.7 5.959 7 0.6 0.549 0.896.9.45.895.65.57.75.998.0.499 4.09 5.408 8 0.6 0.546 0.889.08.97.860.06.449.64.896.085.55.8 5.04 9 0.6 0.54 0.88.00.8.8.6.98.574.8.998.50.690 4.78 0 0.60 0.54 0.879.09.7.8.8.59.57.764.9.69.58 4.587 0.60 0.540 0.876.088.6.796.0.8.49.78.879.06.497 4.47 0.59 0.59 0.87.08.56.78.79.0.46.68.86.055.48 4.8 0.59 0.58 0.870.079.50.77.60.8.46.650.80.0.7 4. 4 0.58 0.57 0.868.076.45.76.45.64.45.64.77.977.6 4.40 5 0.58 0.56 0.866.074.4.75..49.97.60.746.947.86 4.07 6 0.58 0.55 0.865.07.7.746.0.5.8.58.74.9.5 4.05 7 0.57 0.54 0.86.069..740.0.4.68.567.706.898..965 8 0.57 0.54 0.86.067.0.74.0.4.56.55.689.878.97.9 9 0.57 0.5 0.86.066.8.79.09.05.46.59.674.86.74.88 0 0.57 0.5 0.860.064.5.75.086.97.6.58.66.845.5.850 0.57 0.5 0.859.06..7.080.89.8.58.649.8.5.89 0.56 0.5 0.858.06..77.074.8.0.508.69.89.9.79 0.56 0.5 0.858.060.9.74.069.77..500.69.807.04.768 4 0.56 0.5 0.857.059.8.7.064.7.07.49.60.797.09.745 5 0.56 0.5 0.856.058.6.708.060.67.0.485.6.787.078.75 6 0.56 0.5 0.856.058.5.706.056.6.96.479.605.779.067.707 7 0.56 0.5 0.855.057.4.70.05.58.9.47.598.77.057.690 8 0.56 0.50 0.855.056..70.048.54.86.467.59.76.047.674 9 0.56 0.50 0.854.055..699.045.50.8.46.586.756.08.659 0 0.56 0.50 0.854.055.0.697.04.47.78.457.58.750.00.646 40 0.55 0.59 0.85.050.0.684.0..50.4.54.704.97.55 50 0.55 0.58 0.849.047.99.676.009.09.4.40.59.678.97.496 60 0.54 0.57 0.848.045.96.67.000.099..90.504.660.95.460 80 0.54 0.56 0.846.04.9.664.990.088.09.74.486.69.887.46 00 0.54 0.56 0.845.04.90.660.984.08.0.64.475.66.87.90 000 0.5 0.55 0.84.07.8.646.96.056.7.0.47.58.8.00 07 Noth Cosotum UK Ltd. Pg 4 o 4